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    Potential Scenario
    118

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    Potential Scenario
    136

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    79

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    Modeling Scenario
    219

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    209

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    4-050-ResonanceBeats-ModelingScenario
    We study what can happen when a pure oscillator (no damper) is driven by a forced vibration function which has the same or close to the same natural frequency as the system it is driving.
    Modeling Scenario
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    182

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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
    Free Online Textbook
    210

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    Modeling Scenario
    388

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    1-076-ClimateBifurcation-ModelingScenario
    We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
    Potential Scenario
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    59

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    Modeling Scenario
    293

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    1-098-NeuronDetection-ModelingScenario
    Students study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can help understand basics of neural dynamics. The modeling framework is known in mathematical neuroscience as ``integrate-and-fire''...
    Potential Scenario
    116

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    35

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    2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
    Walk through the cases in context of second order linear constant coefficient differential equation with driving function
    Article or Presentation
    179

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    51

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    2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
    We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.
    Modeling Scenario
    389

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    257

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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Potential Scenario
    242

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    36

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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    Potential Scenario
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    46

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    2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function
    This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.
    Potential Scenario
    147

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    81

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    2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
    Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
    Modeling Scenario
    637

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    544

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    0

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    1-032-WordPropagation-ModelingScenario
    This activity is a gentle introduction to modeling via differential equations. The students will learn about exponential growth by modeling the rate at which the word jumbo has propagated through English language texts over time.
    Modeling Scenario
    391

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    167

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    7-008-MachineReplacement-ModelingScenario
    Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
    Article or Presentation
    168

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    46

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    Potential Scenario
    160

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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = (t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
    Potential Scenario
    130

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    50

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    2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
    We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.
    Potential Scenario
    147

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    31

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    0

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    2011-W_Wood-Squigonometry
    The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.